Assimilation can occur either spontaneously or forcibly. In the case of the Romans, they forcibly created assimilated weaker cultures and had the weaker culture adopt their language and other cultural practices. 

The four factors for determining assimilation are: socioeconomic status, geographic distribution, second language adoption, and intermarriage. This determines the level that an immigrant assimilates within a culture. 

Multiculturalism is the term that describes the promotion of multiple cultures within a society. In America, this idea became an important part of society in the 70's and 80's when African Americans and Latinos were working to get recognized. 

Acculturation is the term for the process of change that occurs after two cultures meet. Acculturation can have effects in areas of the two groups' culture, customs and social habits. These changes can also occur at an individual level. 

The only belief system mentioned in this question that was founded by Confucius was Confucianism, which included philosophical and ethical beliefs and ways of thinking.

Although all of these nations have an Islamic majority, the question asks which of them is the “cultural hearth.” A “cultural hearth” is a point from which a widespread culture originates. Islamic culture is widespread around North Africa and the Middle East - and can be found in many other areas of the world as well. But, the point of origin for this culture is Mecca and Medina, two cities found in modern-day Saudi Arabia.

All of these are considered macro-cultural regions of Asia except “Central Steppe.” The Central Steppe is a term that could theoretically be used to describe the Great Plains, or “steppes,” of Central Asia (such as Mongolia), but most of this territory falls under the broad category of “Sino-Japanese.”

The continent of Africa is fairly evenly divided between Islamic (in the North of the continent) and Sub-Saharan African. The Islamic macro-cultural region also includes much of the Middle East. Although it is true that the continent of Africa is divided between a Muslim dominated north and a Christian dominated south, “Christian” is not the name of a macro-cultural region that is frequently used by cultural geographers.

The “Conquest Theory” was developed to explain the dominance of the Indo-European language family. More than half of the world’s population speaks some form of an Indo-European language. According to the Conquest Theory this is because the original speakers of this language group spread westward, rapidly overpowering previous inhabitants of much of Europe and Asia. The people of this region then, several hundred years, spread outwards around the world conquering new territories and spreading their languages to new continents.

Some cultural geographers divide the world into a series of macro-cultural regions. The “Slavic” culture is found predominantly in Eastern Europe and Russia. Other "macro-cultural" regions include Anglo-America, Western Europe, South Asia, and East Asia.